So I'm trying to prove that any five points, of which no 3 are colinear, there is a single conic that passes through al of them. I don't want to use projective geometry but rather, only analytic geometry.
Clearly I have to start out with the equation $Ax^2+Bxy+Cy^2+Dx+Ey+F=0$ and substitute, but I don't know what to do afterwards.